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Function Worksheet - Page 2

Function Worksheet
  • Page 2
 11.  
Ed earns $p per hour working as a translator. He must work for h hours to earn $325. Which of the following equations best relates the variables?
a.
p = h325
b.
h p = 325
c.
h = p325
d.
hp = 325


Solution:

Ed earns $p per hour.

To earn $325 he has to work for h hours.

If he works for 1 hour he earns $p, so if he works for h hours he earns $hp.

So, hp = 325.


Correct answer : (4)
 12.  
Find the constant of variation in the direct variation model y = 6x.
a.
- 6
b.
6
c.
1
d.
1 6


Solution:

The direct variation model is y = kx, where k is the constant of variation.

In the model y = 6x, k = 6.
[Compare with y = kx.]

Therefore, the constant of variation in the direct variation model y = 6x is 6.


Correct answer : (2)
 13.  
Cost of a chocolate is $0.35. Identify the graph that shows the relationship between the number of chocolates and their total cost.

a.
Graph 3
b.
Graph 2
c.
Graph 4
d.
Graph 1


Solution:

Let x be the number of chocolates.

As the number of chocolates increases, the total cost of the chocolates also increases.

The direct variation between the number of chocolates and its total cost can be given as, total cost = 0.35 × x.


The number of chocolates and the total cost is given in the table.

Graph 1 shows the relationship between the number of chocolates and its total cost.


Correct answer : (4)
 14.  
A machine can make 1,500 bolts in 3 hours. Which graph shows the relationship between the number of bolts produced by the machine and the time taken?

a.
Graph 4
b.
Graph 3
c.
Graph 1
d.
Graph 2


Solution:

The number of bolts produced by the machine in 1 hour = 1500 / 3 = 500.

As the time goes on, the total number of bolts produced by the machine, increases.

The direct variation between the number of bolts produced by the machine and the time taken can be given as, number of bolts produced in x hours is 500 × x.


The number of bolts produced and the time taken is shown in the table.

Graph 4 shows the relationship between the number of bolts produced by the machine and time taken.


Correct answer : (1)
 15.  
The table shows the relationship between the number of hours it takes to complete a task and the number of workers doing it.

Number of Workers2489
Number of Hours36189?

How many hours would it take for 9 workers to complete the task?
a.
9
b.
7.2
c.
8
d.
6


Solution:

From the table, 2 workers take 36 hours to complete a task, 4 workers take 18 hours to complete the same task and 8 workers take 9 hours to complete that task.

2 × 36 = 4 × 18 = 8 × 9 = 72 hours are needed to complete the task for 1 worker.

Time to complete the task for 9 workers = 72 / 9 = 8 hours.


Correct answer : (3)
 16.  
Identify an equation that shows an inverse relation between x and y. Assume y = 5 and x = 10.
a.
y = 5 10 x
b.
xy = 5 10
c.
xy = 50
d.
x = 5 10 y


Solution:

If x and y vary inversely, then xy = k, where k is a constant of variation.

10 × 5 = k
[Substitute the values of x and y.]

k = 50
[Multiply.]

Therefore, the equation that shows an inverse relation between x and y is xy = 50.


Correct answer : (3)
 17.  
Identify a graph that shows an inverse variation.


a.
Graph 4
b.
Graph 2
c.
Graph 1
d.
Graph 3


Solution:

Inverse variation is a relationship between two variables, in which, the product is a constant. When one variable increases the other decreases in proportion, so that the product is unchanged.

In Graph 1, as the values on x-axis increase, the values on y-axis decrease such that the product of any value on x-axis and the corresponding value on y-axis is constant.

This shows that the values of x and y are inversely related.

Therefore, Graph 1 shows the inverse variation.


Correct answer : (3)
 18.  
Identify the graph that shows the relation between the number of workers and the time taken (days) by them to finish a particular job.


a.
Graph 1
b.
Graph 4
c.
Graph 2
d.
Graph 3


Solution:

As the number of workers increase, the time taken by them to finsh the job decreases.

Inverse variation is a relationship between two variables, in which, the product is a constant. When one variable increases the other decreases in proportion, so that the product is unchanged.

Therefore, Graph 4 shows the relation between the number of workers and the time taken by them to finish a particular job.


Correct answer : (2)
 19.  
A machine can make 1,200 rugs in 3 hours. Which graph shows the relationship between the number of rugs produced by the machine and the time taken?

a.
Graph 2
b.
Graph 3
c.
Graph 1
d.
Graph 4


Solution:

The number of rugs produced by the machine in 3 hours = 1,200.

As the time goes on, the total number of rugs produced by the machine, increases.

The direct variation between the number of rugs produced by the machine and the time taken can be given as, number of rugs produced in x hours is 400 × x.


The number of bolts produced and the time taken is shown in the table.

Graph 3 shows the relationship between the number of rugs produced by the machine and time taken.


Correct answer : (2)
 20.  
Sarah is paid $26 for every two hours of babysitting. Which of the graphs best represents the situation?

a.
Graph 4
b.
Graph 3
c.
Graph 1
d.
Graph 2


Solution:

Let x be the number of hours Sarah babysits.

Amount of money Sarah earns in one hour = $13.

If Sarah babysits for more hours, the amount of money she earns, increases.


Therefore, the direct variation between the number of hours Sarah babysits and the amount of money she earns can be given as, amount of money Sarah earns = 13 × x.

The number of hours Sarah babysits and the amount she earns is given in the table.

Graph 2 best represents the situation.


Correct answer : (4)

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